Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, engineering, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the butterfly effect. Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos.
Chaotic behavior can be observed in many natural systems, such as weather. Explanation of such behavior may be sought through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps.
Read more about Chaos Theory: Chaotic Dynamics, History, Distinguishing Random From Chaotic Data, Applications, Cultural References
Famous quotes containing the words chaos and/or theory:
“Unable to create a meaningful life for itself, the personality takes its own revenge: from the lower depths comes a regressive form of spontaneity: raw animality forms a counterpoise to the meaningless stimuli and the vicarious life to which the ordinary man is conditioned. Getting spiritual nourishment from this chaos of events, sensations, and devious interpretations is the equivalent of trying to pick through a garbage pile for food.”
—Lewis Mumford (1895–1990)
“There could be no fairer destiny for any physical theory than that it should point the way to a more comprehensive theory in which it lives on as a limiting case.”
—Albert Einstein (1879–1955)